To answer your questions
1a. Your marrying now normally should not have any effect on your fiancée’s pending applications.
1b. If you marry, your fiancée doesn’t have to inform the USCIS of her new marital status.
1c. Check the I-751 processing times (they’re available on the USCIS site) to see what cases are currently being processed. If cases with her filing date have already been processed, then she or her attorney should contact the USCIS to check on the status of her case. I-751 petitions are low priority applications and aren’t processed too quickly. Also, presuming that your fiancée requested a waiver of the joint filing requirement, it’s likely that she’ll be called in for an interview.
2a. Your marrying a resident will have no effect on an H-1B renewal. An H-1B visa is a dual intent visa, meaning that you are still eligible for the visa even if you intend to pursue a green card application (through marriage, work, etc.)
2b. Presuming that you’re referring to an employment-based green card application, you definitely can begin the process now.
Attorney Edward Weiner
http://www.immigration-aux-usa.com/